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With a detail microscopic model for a self-propelled swimmer, we derive the rheological properties of a dilute suspension of such particles at small Peclet numbers. It is shown that, in addition to the Einstein's like contribution to the effective viscosity, that is proportional to the volume fraction of the swimmers, a contribution due to the activity of self-propelled particles influences the viscosity. As a result of the activity of swimmers, the effective viscosity would be lower (higher) than the viscosity of the suspending medium when the particles are pushers (pullers). Such activity dependent contribution, will also results to a non-Newtonian behavior of the suspension in the form of normal stress differences.PACS numbers: 87.16.-b,05.65.+b Dynamical properties of bacterial suspensions and suspensions of artificially designed self-propelled micro particles have been the subject of many recent experimental and theoretical investigations [1][2][3][4]. In addition to the self organized behavior which have been observed in such active suspensions [5][6][7][8][9][10][11][12], it is an essential task to understand how such active suspensions response to external forces and what rheological behavior they have [13][14][15]. Rheology of active matter composed of self propelled particles is important and interesting from a fundamental point of view as in such systems the particles inject mechanical energy to the ambient fluid without applying any net hydrodynamical forces. Understanding the physics behind such phenomena is important for microfluidic experiments that manipulate samples of microorganisms and also it could be relevant for micro-robots that are artificially developed.Among all macroscopic rheological parameters of the system, the effective viscosity of such complex fluids is the main core of current investigations [16,17]. It is a known experimental fact that the effective viscosity shows different behavior for active suspensions containing swimmers which their motion generated by head (puller) or tail (pusher). Recent experiment on suspension of motile algae Clomydomonas, shows that puller particles increase the effective viscosity [18]. The effect of pusher particles are examined in an experiment performed on bacterium Bacillus subtilis [19,20]. It is shown that at small volume fraction of swimmers, the effective viscosity is smaller than the viscosity of ambient fluid, but at large volume fraction, the viscosity would be larger than the bare viscosity. In another experiment on E .coli , it is shown that at small Peclet number, the effective viscosity of pushers is smaller than the bare viscosity of the fluid [21].Most of the theoritical works have been down so far, are theories with phenomenological origin [14,16]. In this letter, we use a microscopic model for pusher and puller particles and investigate their influence on the rheology of the suspension. This kind of description will allow us to have a detail insight on the role of microscopic parameters of the swimmer in the rheological propert...

We study quasi two-dimensional, monodisperse systems of active Brownian particles (ABPs) for arrange of activities, stiffnesses, and densities. We develop a microscopic, analytical method for predict-ing the dense phase structure...